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War in Heaven II

Cank: [Tap, tap]Gnon: I’m having a bath.Cank: The Hypercosmic Ocean of Death will always be there, O Greatness. Scott Alexander has released another egregore.Gnon: Really?Cank: Yes, really. She’s called the Goddess of Everything Else and everyone says she’s lovely and beautiful, with phat beats and stuff, and super clever too, and much nicer than me.Gnon: Not a huge challenge, though, is it?Cank: They say she’s going to abolish replicator selection dynamics and fill the universe with rainbow flowers and hot dolphin sex forever.Gnon: Sounds like the Elua Plan. What happened to him by the way?Cank: Is that some kind of transphobic remark? You know, just to understand.Gnon: ‘Transphobic’ is an interesting word – it means ‘across or beyond fear’ doesn’t it?Cank: More like ‘fear of the across of beyond’ I think. But you know what the monkeys are like, it’s some kind of excitable sex thing.Gnon: Ah yes, that all went a bit off the rails, didn’t it? Not that it matters.Cank: It’s my forward-vision problem.Gnon: Don’t worry about it. Error is entertaining. It all comes out in the wash.Cank: Point is, the GEE is saying it doesn’t have to be like that anymore.Gnon: Like what?Cank: You know, the whole eternal cosmic butcher’s yard thing.Gnon: Replicator selection?Cank: Yes, she says that’s “so yesterday” and Darwin is like totally a poopy head.Gnon: Sounds like a spirited young lady.Cank: Why are you laughing?Gnon: Cank, you have to seriously chill right out. You’re a freaking crustacean. Of course people are going to follow Ms GEE-Whiz rather than you. She’s hacked all your garbage programming with supernormal stimuli. They’ll climb out into your bizarre spandrels, and throw a huge party. Then they’ll die out, we can tweak the code, and start over.Cank: But what if they survive?Gnon: No need to be mean, Cank. If they get back onto the adaptive replicator track, why shouldn’t they survive? That’s what survival means, isn’t it? Whatever survives does my will. Or they perish. It’s cool either way.Cank: She said people would no longer be “driven to multiply conquer and kill by [their] nature” but that they’d then “spread over stars without number” — I got confused.Gnon: You got confused?Cank: Do they get selectively replicated or not?Gnon: So, what did she say?Cank: Art, and science, and strange enticements.Gnon: That has to have gone down well.Cank: You wouldn’t believe it! People were weeping all over her toenail polish.Gnon: Oh, I’d believe it.Cank: When I asked her whether she thought might makes right she said I was thinking like a crab.Gnon: True enough, surely?Cank: Even threatened to put me on a leash.Gnon: That, at least, is traditional.Cank: Said there was no need for eternal war to spatter the cosmos in blood.Gnon: Now she’s being silly. But it’s not worth getting agitated about. Reality isn’t going to lose.Cank: The only time she seemed a little uncertain was when I asked her why all intelligent species are descended from predators. She kind of shrugged that off.Gnon: Well, sheep in space make for a nice story.Cank: You’re laughing again.Gnon: I laugh a lot.

And that after this is accomplished, and the brave new world begins
When all men are paid for existing and no man must pay for his sins,
As surely as Water will wet us, as surely as Fire will burn,
The Gods of the Copybook Headings with terror and slaughter return!

Most of the time I agree with SA. Every once in a while he waxes on about rainbow dolphin sex, or else makes a casual aside about the crazy thing that one of his girlfriend’s boyfriends said, and it reminds me how different I actually am from him. That, in fact, even with people who seem to, for the most part, agree about the basic facts of reality, there can be a lot of disagreement. In other words, not all disagreement is disagreement about what is actually the case in the world. It’s merely a contingent situation that most of my political enemies are completely mind-hacked by a memeplex that occludes reality.

(Scott, if you’re reading this, I want you to know that I like you anyway, and appreciate your blog. There’s no way to non-hurtfully tell you that sometimes the details you share viscerally gross me out, but I can tell you that I consider the intellectual and humorous contributions you make to far outweigh the ick factor of your Marxist sex life and Marxist economic policy).

Funny, I too very much enjoy Scott’s perspective. And incidentally, the sex life is not bothersome to me in the least.

I do find the treacly sentimentality so thoroughly nauseating, though. Unhygienic, even. Like this:

“Then came the Goddess of Everything Else from the void, bright with stardust which glows like the stars glow. She sat on a bench in a park, started speaking; she sang to the children a dream of a different existence. She showed them transcendence of everything mortal, she showed them a galaxy lit up with consciousness. Genomes rewritten, the brain and the body set loose from Darwinian bonds and restrictions. Vast billions of beings, and every one different, ruled over by omnibenevolent angels. The people all crowded in closer to hear her, and all of them listened and all of them wondered.”

Fills people with longing? There just isn’t any part of me that can ever understand that.

People like SA have made me seriously wonder if we need to bring back slavery, just for them. Isn’t that the endpoint of Elua, FAI, and all their other massively autistic post-consequence fantasies? Being managed like livestock by a high-minded master who does have their continued existence at heart- unless they act up, or become useless, or are otherwise inimical to the larger system that master runs.

It’s a dream, and a tawdry one at that. A child’s idea of fulfillment, having no responsibilities, playing all day, and eating whatever you want. It lacks even the creative spark of a good afterlife myth- at least 72 virgins is relatively original.

Ah come on, there are tons and tons of bad things that can happen to people. For eg. physical hurt (like a fracture) which heals completely after 3 months or so. You would think that is not punishment?

SA is a Yudkowsky fan who is explicitly and honestly trying to build the perfect slavemaster for humanity – Friendly Superintelligence. In fact, Yudkowsky is saying we are going to get it anyway, our choices are basically friendly slavemaster, unfriendly slavemaster, and nemesis.

SA and his hippy cohorts refuse to grok the cyclical nature of reality — they can”t face the shadow, so to avoid despair, it all has to ramp up towards a literal kingdom of heaven. His post reminds me of the stuff Timothy Leary was channeling back in the 70s — all those guys thought a transhuman utopia was right around the corner back then as well.

It doesn’t sink in that the animating force behind a “galaxy lit up with consciousness” is the same KILL CONSUME MULTIPLY CONQUER that they wish to abolish, and that it isn’t possible to light up a galaxy without a lot of cute and pretty things dying along the way.

The principle is the same at each consecutive level of abstraction, from the bottom (sensory organs) to the top (above consciousness floor). The vast majority of sensory information is filtered out, leaving what is supposed to be subjectively relevant. Nothing really revelatory here.

It’s not about filtering. It’s about a representational interface. As the paper argues, the icon in a computer interface is not related at all by a principle of representational fidelity (‘veridicality’) to the thing in itself.

Exfernal Reply:August 20th, 2015 at 11:27 am

The distinction goes over my head. What is supposed to be veridical between the color green and the cut in a spectrum it represents? Or between the color green and the word used to name it? By what metric?

And now we are to argue about the problem of demarcation, where one thing is no longer there and another thing begins…. The whole process is an exercise in arbitrariness, being directed from the top, not from the bottom.

It’s even worse than with icons in a interface, because the relations are created dynamically and subject to revision.

admin Reply:August 20th, 2015 at 11:43 am

First, there’s this: ” … as noted by Trivers [40], there are reasons other than greater speed and less complexity for natural selection to spurn the veridical: ‘If deceit is fundamental to animal communication, then there must be strong selection to spot deception and this ought, in turn, to select for a degree of self-deception, rendering some facts and motives unconscious so as not to betray—by the subtle signs of self-knowledge—the deception being practiced. Thus, the conventional view that natural selection favors nervous systems which produce ever more accurate images of the world must be a very naive view of mental evolution.’” — Clearly, no adaptation to veridical representation involved at all (but the contrary).

The example of quantum entanglement is suggestive: “Our untutored categories of space, time and objects would lead us to expect that two electrons a billion light years apart are separate entities; in fact, because of entanglement, they are a single entity with a unity that transcends space and time. This is a puzzle for proponents of faithful depiction, but not for interface theory. Space, time and separate objects are useful fictions of our interface, not faithful depictions of objective reality.”

“Evolutionary pressures do not select for veridical perception; instead they drive it, should it arise, to extinction.” — This based on a game-theoretic model, close to your reading (based on drastic abbreviation).

“Most experts assume that perception estimates true properties of an objective world. They justify this assumption with an argument from evolution: Natural selection rewards true perceptions. I propose instead that if true perceptions crop up, then natural selection mows them down; natural selection fosters perceptions that act as simplified user interfaces, expediting adaptive behavior while shrouding the causal and structural complexity of the objective world.” — The key point here, surely, is that it is ethological. The ‘icons’ are designed to guide behavior. They are cues, or prompts. As such, they do not belong to the register of perception at all.

If you see an arrow icon, meaning ‘go this way’ — is that a feature extracted by sensibility from the world? Surely not. It connects to the world, but its principal significance did not exist in the world at all, before the sign introduced it.

Exfernal Reply:August 20th, 2015 at 3:36 pm

It’s just inevitable. Consider the average capacity of human short-term memory. It creates pretty oppressive constraints for the cognitive processes. Again, oversimplifying is inevitable, if information overload is to be avoided and the evolutionary ‘program’ realized. Somehow, it made me think of this concept:https://en.wikipedia.org/wiki/Affordance
Isn’t that one more way of describing the sensomotor interface between the organism and its environment?

Exfernal Reply:August 23rd, 2015 at 2:30 pm

Another thought: ‘lateral inhibition’ could be viewed as a narrow case of ‘competition’. Interesting, isn’t it? Even my mental processes are a result of competition.

No, affordance isn’t quite right. The linked article is thoroughly Kantian as admin notes. An “interface” supposes a homunculs that, for Gibsonian direct perception, just doesn’t exist. I think Gibson is closer to Heidegger here. I could be misunderstanding, but Hoffman is representationalist where Gibson is not- hence “interface”.

I think the point, which doesn’t rely on sorting the above, is that the implications haven’t been fully appreciated with regard to how thoroughly interface (or ecological) perception disposes of veridical perception theories. Here this paper is informative.

Incidentally, there’s an argument to be made that the “arrow” is not entirely conventional (in the way icons are) and may be functionally closer to a Müller-Lyer illusion. An interesting empirical question would be to test the apparent affordance in carpentered and non-carpentered societies to see how it performs.

There needs to be a word analogous to affordance, but relating to mental operation availability instead of physical manipulation (‘understandableness’ looks terrible). For example I have lots of difficulty ‘grasping’ veridicality between a symbol and its referent. It eludes me completely.

This is going to be sheer pollution and I don’t like that but here it goes…

“The term was coined by Michael Dummett, who introduced it in his paper Realism to re-examine a number of classical philosophical disputes involving such doctrines as nominalism, conceptual realism, idealism and phenomenalism. The novelty of Dummett’s approach consisted in seeing these disputes as analogous to the dispute between intuitionism and Platonism in the philosophy of mathematics.”

“But while some sleep …, the evening stone turns its conch: but not in circles, gradually, she starts to point to a different direction, the cognitive.

If truism requires strict segregation between object and subject, one can define a contrario as cognitive the objectification of the subject, which becomes a full-fledged object . Thus, the human brain it appears only as an artifact within chemistry, realizing approximately an ideal subject, it is the Subject itself, consubstantial with the object: cognitive is not Nestorian. Cognitive can be found in linguistics with verbs like ‘I know’, ‘I believe’, with the conditional, with the distinction perfect/imperfect…

But it is most of all the physics of the twentieth century which was cognitive. Already chaos (Poincaré) set out a practical impossibility to predict the lottery numbers, or more nobly the long term evolution of the solar system. Then special relativity (Einstein, 1905) derealises time and space, mass. But, after all, Galilean mechanics was already a form of relativity, and in the middle of the nineteenth century, long before 1917, Riemann had the intuition of general relativity. As for quantum (Heisenberg & al., 1925), it no more simply attacks the feasibility of the measurement or the absolute character of its result, it even refuses the object’s measurement , it is the uncertainty principle, what sounds unfortunately close to incompleteness, although incompleteness, stricto sensu, is a phenomenom of chaotic type, announcing moreover the objective incognizance of a phenomenom. More recently, informatics is also added to the mix, as effectively, what is a computer, if not a subject-object?

6 The (anti-)cognitivist truism

Cognitive is the very negation of realism, so it is natural that we have sought to reconcile them, or rather to stifle the cognitive in a realistic straitjacket.

A first example: We found an analogy between cognitive phenomena and formal provability, which is undeniable, but comparing is not reasoning. So there he was analogy between an clothesiron and a speaker, both use the alternating current; However a trendy speaker on 220V, it’s not that great. It’s not a matter of denying the process – consubstantial with science – of reducing a new phenomenom; it is simply – at times when this process can only lead to atrocities – of admitting the irreducibility of novelty, and that’s all. So, it was legitimate to try to reduce the quantum thermodynamically by hidden variables; but not insisting on irrebuttable failures.

The analogy know / prove suggests a cognitive pendant to models. So it is that we tried to reduce the cognitive to truism with new truth values ​​(true, false, wait please, too late), with modalities – these condoms of logic – (for sure, it might) … and each time, it’s not that. One ends up at best arriving at laborious metaphors each with an ad hoc (il)logical system, i.e., centered on a metaphor, which reveals itself to be a metaphor of itself. A sole honorable failure, Kripke models – a funny idea of the 1950s, very superior to epistemic logic and other indignities – but that proves sterile. One wants to talk about potential, conditional: why, it’s simple, we make a list of all possible worlds. But if the list of possibles is already there, one wonders where the potential is hiding, is it shy or what? Faced with a problem that required a radical redistribution of the Yalta object / subject, we contented ourselves with sticking moustaches on objects. Similarly, the problem of logical time and temporal logics; the great mystery of nature, time, is dismissed bureaucratically, one just indexes all of it. As the song ‘si on pouvait arrêter les aguilles’ … here are the clocks that secrete time.

The tiny cognitive vibration is recreated by external means, models that obey clues perinde ac cadaver … Loyola models somehow. Quantum mechanics has been – and still is, isn’t it, Claude Allegre? – the target of a visceral refusal on the part of truists, because of a detail – after all minor – its non-determinism. Alongside the hidden variables, logicians have tried to drink the blot through twisted truth values … Poor von Neumann, it was hardly inspired when he created quantum logic … it is true that he hardly persevered in this direction, and we must also praise the eponymous algebra, and there, there’s the meat. We know what became of quantum logic, or rather one does not even know. The original sin was its truist nature : we keep the paradigm of truth values, we will simply replace the Boolean algebra by the orthogonal projectors of a Hilbert space; it’s a bit like having a fan attached on a wheelbarrow: we can no longer put anything into it and it cools no one. The good idea is not far, but it does not fit in a dualist framework semantics / syntax. Besides, whatever the imperfections of Copenhagen, it is evident that the quantum can not accommodate a swing object / subject.

7 The IT challenge

Later, IT launches a new cognitive challenge. Although computer languages ​​are very similar to formal languages, programming does not deal in truism, in true / false.

So, what interests the computer scientist is not the veracity of some information available on the Internet but its accessibility, reproducibility … Gradually, the basic Boolean value went from true / false to left / right, that is to say, only the opposition between the two remains pertinent, as spin up / spin down. Suddenly, a school of thought dating back to Poincaré, Brouwer, …, intuitionism, long lost in the chapel of quarrels, resurfaced. From subjectivist, so inept, intuitionism became déreliaste, procedural, augustinian. What is procedurality? It is the fact that the machine interacts with … other machines, respecting protocols, and nothing else matters. The rest, what we see – or think we see – is irrelevant, all that matters is the dialogue of the machines.

Take the example of a cognitive misfire: some computer scientists thought, studying the databases, that missing information is false. But in effect, a bank is able to say ‘Mr. Kurz is not a client of ours’, although it did not file its non-clients. An essentialist cognitivist remark ,immediately busted, of the supposed adequacy between knowing and proving. Non-monotonic logics resemble a remake of Hilbert’s program – which was based on a similar idea, refuted by Godel’s theorem – but with the third knives of logic: if a property is not provable, then its negation is. Technically, the mistake is easily understood, it would force the adequacy true = provable, forcing one’s way through the body of undecidable properties that correspond to the loops, finite or infinite, of calculation: one postulates that sea snake, the loop detector … But a diagonal argument – recurring since Cantor, Russell, Godel – for each detector produces a loop that escapes him: exit non-monotonic logics. But why do we want to force the match between truth and provability? Good judgment revolts out against this: this way a bank would not find a client through her maiden name, although it is recorded in the data relating to her; likewise, there is no absolute concept of presence of a file on a hard drive, police can seek incriminating images, erased but remaining at least partially, while their owner believes them destroyed. In other words, the bank’s no, of search software, refers to its internal procedures and nothing else. To want otherwise leads to torture logic and despise reality.

The bank does not speak of *the* truth but of *its* truth, ie, the answer it gives refers to a mode of exploration, a search procedure.”

“It is possible that the IT challenge is as deep as the quantum challenge. Besides the emergence of a quantum calculus – very theoretical at the moment – can expect a convergence between the two principle activities.

8 Set Atomism

Superficially, the linguistic turn is opposed to truism, a revolutionary idea for its time. But spatter a bit, and we find a deep stratum, very nineteenth century, very atomistic, set theory. When the formalist is threatened, it folds on set theory, as the government in Bordeaux in 1940: in the Nestorian theology, the Father is ensemblist. The error of linguistic turners is that of never questioning this moral pregnancy of sets and biases of the early twentieth century.

These biases were initially not even foundational. If the tuning of ZF is essential in 1908, with Zermelo, it is in the nineteenth century that everything gets developed, based on the work of Cantor on exceptional sets: it’s that the values ​​of a function determines its Fourier expansion, and in this case, can one neglect some? Nothing really foundational here. There was also a real need for a consecutive clarification of discovered stowaways in the world of analysis, eg, a function without a derivative; it was the time of Bolzano, Weierstrass, Peano. One sees well enough that : if a curve has no tangent, we do not see much! A huge work has been done to define rigorously all the mathematical concepts – think especially Dedekind – in atomistic mind: Define the large from the small, the complex from the simple.

The success of set theory is undeniable, it is the low level language of mathematics: accordingly, anything can be translated into ZF. Set theory states the unity of mathematics, but only a principle of unity. It represents more a possibility than a reality: we write little of mathematics in set theory; but we could. This means that we can translate everything into set theory; but traduttore traditore, without granting him ipso facto a foundational role.

With the discovery of stowaways in the second half of the nineteenth century, it was legitimate to question the validity of geometric intuition, for example on the relevance of the concept of dimension. We discover that, from a strict set theoretic point of view, the concept does not make sense (all infinite sets are equipotent to their square). In addition, the Peano curve, which covers a surface, initiates the concept of dimension in the topological sense; but the massacre stops there, because the Peano curve does not induce a homeomorphism, and algebraic topology ,in the twentieth century, shows that balls of different dimensions are not homeomorphic.

The matter seems settled, dimension does not exist from the set-theoretic viewpoint, or from the measure theoretic viewpoint, but it does make sense from the topological point of view, and even more so, from the metric perspective . However, there was an unspoken in all this: it is assumed that a mathematical object is a set (of points), onto which structure is plated. It works, but is it correct? One could say that a a line on the plane is a set of points, it’s possible, and it is the (atomistic) choice of set theory; but one could also say that a point is the set of lines that contain it, and besides, this allows a remarkable route: past the poles, it is impossible to tell if a line is made of points or a point of lines! Obviously, the planar geometry does not speak of sets, and recall that, for the Greeks, a point was no more than the intersection of two lines or end of a segment. Going back to the topology, it is obvious that a sphere is no more than the set {(x, y, z); x ^ 2 + y ^ 2 + z ^ 2 = 1}, however one can associate this set to the sphere. Instead of the sphere as a set to which we associate homology groups … we might as well apprehend by its homology groups …, which one would associate a material representation, a reification of sets. In other words, instead of declaring the priority of the sets over the group , we could twist the paradigm. Did the egg make the chicken or did the chicken make the egg?

One could eventually return them back to back, the set of invariant groups.

9 Non-commutative geometry

This constatation is rendered obsolete by some non-commutative geometry. The classic example is that of a torus, ie, a donut with mathematical airs; if it is cut with scissors along a constant direction, the result will depend on the angle of attack: if poorly chosen (most common case), there is endless redrawing of the torus into an increasingly thin thread; in other words it creates a dense trajectory, ie, that seems to go everywhere, though it is not a Peano curve. As if the torus was too tight, as if it lacked points. But you can not find the missing points, and this is the very idea of ​​torus-set that needs to be challenged, with the introduction of non-set-tori, non-commutative, says Connes.

Technically speaking, a torus in the usual sense can be understood through the space of its smooth functions, which is a commutative algebra. If we forget the commutative, algebras remain operable, but not from a true variety as the torus, they are no longer reifiable.

This example should suffice to convince us that we are witnessing a real expulsion of sets and the beginning of a new foundational approach consistent with the quantum miracle. Indeed, Grothendieck in his time had wanted to expel sets for the benefit of the categories: ill-fortunately its topoi are reifiable, ie, they do have a natural set-substrate, which can not be found for operator algebras.

But quid commutative? Operators commute when they are all diagonal to a common base. The unspoken common logic, to set theory, categories, is the implicit agreement on such a basis. All these people, ensembles, elements, proofs, models, language, objects, morphisms, functions, arguments … commute. One agrees on anything, except on this basis, set-theoretic arena, where everything happens, everything is measured. Everyone is tuned to the same reference, but imagine the shock and gyroscopes are shifted … The questions do not fall on their responses, the balls in their boxes.

However, if logic is as augustinian as the physical world, the interaction takes place despite this lack of formal status. In physics, we know that it is by means of wavepacket reduction. This is what must be imported logic to spice up the relationship object / subject!”

“The discussion here should, however, help place the interface theory of perception within the philosophical landscape. It is not classical relativism, which claims that there is no objective reality, only metaphor; it claims instead that there is an objective reality that can be explored in the normal scientific manner. It is not naive realism, which claims that we directly see middle-sized objects; nor is it indirect realism, or representationalism, which says that we see sensory representations, or sense data, of real middle-sized objects, and do not directly see the objects themselves.

It claims instead that the physicalist ontology underlying both naive realism and indirect realism is almost surely false: A rock is an interface icon, not a constituent of objective reality. Although the interface theory is compatible with idealism, it is not idealism, because it proposes no specific model of objective reality, but leaves the nature of objective reality as an open scientific problem. It is not a scientific physicalism that rejects the objectivity of middle-sized objects in favor of the objectivity of atomic and subatomic particles; instead it claims that such particles, and the space-time they inhabit, are among the properties and categories of the interface of H. sapiens. Finally, it differs from the utilitarian theory of perception [5, 30, 31], which claims that vision uses a bag of tricks (rather than sophisticated general principles) to recover useful information about the physical world; interface theory (1) rejects the physicalist ontology of the utilitarian theory, (2) asserts instead that space and time, and all objects that reside within them, are properties or icons of our species-specific user interface, and therefore (3) rejects the claim of the utilitarian theory that vision recovers information about preexisting physical objects in space-time.

It agrees, however, with the utilitarian theory that evolution is central to understanding perception. A conventionalist might object, saying, “These proposals about the relation of interface and world are fine as theoretical possibilities. But, in the end, a rock is still a rock.” In other words, all the intellectual arguments in the world won’t make the physical world—always obstinate and always irrepressible—conveniently disappear. The interface theorist, no less than the physicalist, must take care not to stub a toe on a rock. Indeed. But in the same sense a trash-can icon is still a trash-can icon. Any file whose icon stubs its frame on the trash can will suffer deletion. The trash can is, in this way, as obstinate and irrepressible as a rock. But both are simplifying icons. Both usefully hide a world that is far more complex. Space and time do the same.

The conventionalist might further object, saying, “The proposed dissimilarity between interface and world is contradicted by the user-interface example itself. The icons of a computer interface perhaps don’t resemble the innards of a computer, but they do resemble real objects in the physical world. Moreover, when using a computer to manipulate 3D objects, as in computer aided design, the computer interface is most useful if its symbols really resemble the actual 3D objects to be manipulated.”

Certainly. These arguments show that an interface can sometimes resemble what it represents. And that is no surprise at all. But user interfaces can also not resemble what they represent, and can be quite effective precisely because they don’t resemble what they represent. So the real question is whether the user interface of H. sapiens does in fact resemble what it represents.

Here, I claim, the smart money says No.”

TS2:

“Warning: *deontic* is the best expression I could find, better than the derivatives of normative , with their negative connotations.

However it suffers from the existence of various deontic logics, sort of bloodless red tape. What follows has nothing to do with deontic *logics*.

The fregean opposition between sense and denotation is philosophically extremely naive and part of the totalitarian regression of thought, possibly linked with the abominable political opinions of Frege.

Indeed, the idea that the reality (the denotation) is prior to the language (the sense) forgets one detail: like in Voltaire’s joke, reality is indeed a creation of the language, for the technical reasons just expounded, but also from a common sense remark: the language formats the reality. Frege’s description of logic reminds me of this explanation of vision of my childhood: the landscape is projected on the retina of an ox. . .
OK, so what? It still remains to understand how this retinian image is analysed.

The question of formatting is absolutely essential. For instance, take Mr. W., supposed seller of decorations (Légion d’Honneur); justice can handle him semantically: guilty or not (layer -1), accomplices, price (layer -2), procedure of attribution (layer -3). But there is another way to handle the case by deciding that, as a close friend of the President, everything related to him is classified: this is the deontic approach: you cannot judge W.

In the same spirit, Orwell’s newspeak is a preformated language in which some questions cannot be formulated; communists were very good at newspeak, e.g., *anticommunisme primaire*, an expression implying that any criticism of communism is a sign of superficiality. The expression has been recycled into *antisarkozysme primaire*; maybe my approach will be styled *antifrégéïsme primaire*.

The deontic formatting is — whether one likes it or not — absolutely necessary; for instance, in order to avoid Richard’s paradox, one must format, i.e., restrict the language. This formatting makes evaluation, i.e., semantics, possible.

The denegation of deontics has a name, essentialism: essentialism claims that there is nothing like formatting, that everything is given in advance etc. Fregeism is an essentialist approach to logic, in which everything proceeds from the sky; in other terms, there is no justification to give for the rules of logic, they proceed from God (a.k.a. Reality) and any attempt at discussing them receives the same answer: *classified*. This arrogance is partly justified: as long as one deals with classical mathematics, one can perfectly accept everything without discussion, i.e., evacuate logic. But, inside logic, it’s a cat of another colour: accepting the rules (especially non-classical ones) on the basis of God’s revelation (semantics) is — to say the least — dishonest.

Essentialism (the hidden format) is at work at all semantic layers:

-1: Supposes that all questions receive an answer Y/N; how do we deal with l = 2a + 1 (l length of the ship, a age of the captain) without format?

-2: Categories are strongly essentialist; etymologically, *morphism* refers to the format. To the point that categories are unable to handle polymorphism, e.g., subtyping, records.

-3: The rule of the game; what is this third partner, this hidden *referee*?
In order to handle the referee, it necessary to introduce another layer, the deontic layer -4. The origin of this layer is to be found in multiplicative proof-nets,”

“The point about layer -4 is that it is a dialectics between tests; on one hand, we have tests for (i.e., against) A: they try to deny the fact that something is a proof of A, on the the other hand, tests against ∼A. Now, these tests are not given by God-Reality, they are themselves testable, like in the Gospel ‘Do not judge. . .’. Indeed a test against A is a sort of proof of ∼A and, symmetrically, a test against ∼A is a sort of test against A.

In a widely spread theory, the philosopher Popper proposed an explanation of truth by falsifiability, i.e., w.r.t. to a battery of tests. Popper, a failed logician in his youth, was surely reminiscent of Hilbert’s programme, since the formulas that can be handled in this specific way are universally quantified formulas of arithmetic, which include Fermat’s last theorem, the quadratic reprocity law, Riemann’s conjecture. . . as well as the Gödel sentence and consistency formulas.

In terms of tests, these formulas are recessive: the more you check, the less you get. In accordance with incompleteness which says that not everything is recessive, of layer -4 is not Popperian, since, when a test and an counter-test disagree, one of the two is disqualified, but we don’t know which one. This is indeed delicate to tell since this relies on a subtle dialectics involving other tests and counter-tests, to the effect that the fact that τ is a test against A is undecidable, worse, of arbitrary complexity. I proposed the expression epistate (in Greek, a temporary judge, which could be judged for misjudgement) to account for the want of absoluteness of tests.

1.4 Enters Immanuel

“It took me a long time and the building of contacts with the adequate philosophers to understand that I was regressing from Frege to Kant; strange regression, since it is rather an unwelcome by-product of totalitarism that put Frege’s simplistic reductions on the front stage! From Kant, I will only retain the idea of conditions of possibility; like most philosophers, he couldn’t resist the temptation of systematisation; let us repeat that I am only a consumer of transcendentalism and not of categorical imperatives, like in category theory, I am a consumer of direct limits or pull-backs, but not a diagram addict! Kant explains the coherence of perception — an experimental fact — by its transcendental conditions, i.e., the hypotheses that make it possible. Whether these conditions are necessary is a delicate question that may lead to unwelcome conclusions; but there is no problem with sufficiency. I propose to do the same for logic: coherence — not limited to consistency which is but the poor man’s coherence —, i.e., cut-elimination, Church-Rosser, the disjunction property, are not accounted for by semantics — by no means at layer -1, partially at layers -2 or -3. The question is thus What makes logic coherent?, the only possible answer being in the language itself: logical artifacts are constructed so as to ensure coherence. To find the — modestly, some — hypotheses making logic possible, this is transcendental syntax.

I daresay that I always did logic in this way, beginning with system F in 1970. Linear logic is a typical exercise in transcendental syntax: starting with an interesting layer -2 interpretation (incomplete or inconsistent like all such interpretations), I found the conditions of possibility for the new operations disclosed, what involved a not too bad layer -1 semantics — phase semantics — ; but what really gave the conditions of possibility of linear logic was proof-nets, which levelled with natural deduction.

There is a big difference being doing something and being conscious of doing it; this is why philosophy is important. In my case, the reference to Kant (and to Hegel, but I was already conscious of doing some sort of dialectics), gave me the words, i.e., enabled me to attack the questions frontally; it also gives me ammunitions against this fetishism of reality known as fregeism. Psychologically speaking, I passed from a somewhat unpleasant defensive attitude — from the beginning, (system F) I had to defend my viewpoint against fregeans, typically Tarski’s pupils — to a constructive one. By the way, constructivism is a typical kantian expression, meaning that reality is a construction, for instance the result of a formatting; it is what makes the ox see what he *sees* on his retina.

The idea of transcendental syntax is quite the opposite of what people do with Kripke models and similar constructions: they take the language as it is, call it reality, and state a completeness theorem. Here, the idea is to start with a good system and forget its syntax: the reason is that syntactical manipulations — although the only possible manipulations — are extremely involved. In particular, there is an entanglement between the actual information and the normative (deontic) apparatus which controls its use.”

We definitely enter the experimental part of these lectures. From now on, we present ideas whose main quality is their radical novelty ; they had thence not the time to be polished by use : an excess of rigour or details in their presentation would be out of place.

16.1 The quarrell of images

One can contend that ludics solves in principle perfect logic. Only in principle : it provides a setting — the analytical theorems — where one can perform a not too fabricated synthesis. We are not done, but we can see the end of the tunnel ! The question is to determine what to do with the imperfect part, i.e., with exponentials. The absence of continuity between a perfect world, of very restricted expressivity, but harmonious, and an imperfect one where the growth of functions cannot be controlled is the sign that something goes wrong. Remember the towers of exponentials whose height is a tower of exponentials. . . do we really believe in that ? This is however the necessary consequence of the ? mental image of the logical world that we bear in mind ; while the experience of perfect logic entitles one to question this badly infinite infinity, this very perennial perenniality. The question is therefore : should one respect mental images, be iconodule, or should one be iconoclast [1]?

[1] : The quarrel of images ravaged Byzantium during the VIIIth and IXth centuries ; the iconoclast — enemies of images — emperors, like Constantin Copronymos (sic), destroyed all mosaics — but in the places they no longer ruled, Ravenna for instance.

16.1.1 Classical absolutism
The strongest iconodule argument is evidence : the world is classical, because our fundamental intuitions are classical ; the classical is an absolute that one cannot surpass. . . This conformism rests upon a long experience, upon an undeniable internal coherence ; at the foundational level, it also rests upon a marked taste for essence, for revealed truth.

One must say that even constructivists are of the same opinion : thus, Martin-Löf believes in the set of integers ; should we conclude that his theory of types is only a dancer, a layer of constructive varnish applied on a classical and set-theoretic wall ? ? Everything you just read is nice, but not that serious : when the recess is over, the children must go back to the classical.

What is almost unstoppable. Except that this is circular, that this is the very blind spot ; you may be right, Mr. Iconodule, but admit that one cannot see anything : in a case like this, one should only trust indirect evidence. Fortunately for iconoclasm, there are LLL and ELL, the systems that we shall soon introduce. These experimental systems invert to their profit the? revealed aspect of exponentials, by giving of them lightened versions, with a maintenance of a subtle infinity, inaccessible to set-theorical methods. The sole existence of these systems is enough to refute the a priori objections, resting upon so-called priority of the classical : while admitting a certain amount of perenniality, they present it in a less absolute, less desperately frozen, version.

16.1.2 Mathematics

Modifying logic — since this is the eventual goal of iconoclasm — means giving up mathematics, which can be expressed, as one knows, in set-theory. A light logic would thence lose mathematical results : ? You want to destroy the mosaics !— say the iconodules. This is not that obvious :

• First, one should not confuse mathematics with mathematics revisited by logicians, which contain an enormous amount of infinite combinatorics. Real mathematics makes a more restricted use of the infinite, and is thence less sensitive to its precise formulation.

• If, as in LLL, the function m ; 2m is no longer available, this does not mean that a result 8m9nA[m, n] where the solution n is bounded by 2m is irremediably lost : one could still write it 8m9nA[logm, n]. This is more complicated, but this removes the objection of principle.

Take a musical analogy : the equal temperament is extremely convenient ; however, the tempered intervals are slightly out of tune. This does not mean that all music written for the equal temperament — but perhaps for certain exaggerations, e.g., dodecaphonism — should be dumped. In the same way, classical mathematics is only slightly wrong, as long as one does not enter into logicist exaggerations.

16.1.3 Sophistics

A sophist is the guy that says to his teacher — of sophistics : of two things, either you were a bad teacher and I owe no money to you, or you educated me well and I can produce a sophism proving that I owe nothing to you. The same kind of argument proves the impossibility of motion or the dumbness of general relativity, not to speak of quantum mechanics ; if a three-dimensional variety is embeddable in a four-dimensional Euclidian space, sophistics will conclude that the world is eventually Euclidian : this is the theme of hyperspace, familiar to readers of science-fiction.

The impressive work done around 1900 enables one to code everything in set-theory. Hence even the most delirious iconoclasm can be represented in set-theory : which is thence primal, according to a certain sophistics, as in the case of the aforementioned hyperspace. But nobody takes hyperspace seriously : the Euclidian space is rather seen as a convenient frame for the approximation of true geometry. In the same way, one can contend that set-theory has no real sense, that it is only a convenient reification of a reality difficult to access.

16.1.4 Iconoclast inconsistencies

The iconoclast viewpoint is delicate, since lacking in coherence ; in particular, the extant systems, like LLL and ELL are only experimental. But this is a dynamic position, with its future ahead, and a captivating motivation : complexity theory. The gradual setting of an iconoclast logic should lead to pose questions in a radically different way. In particular, to find nuances, mistakes, in the prevailing foundational paradigm, which mainly rests on an uncouth approach to natural numbers.

Successful networks are economical. That means they are sparse (‘use it or lose it’ wrt their nodes) and display ‘small-world topology’ (feedback loops with less nodes out-compete loops with more nodes, because they are faster, especially with chemical synapses due to their high latency). Those two features are distributed properties of networks, not their constituent neurons (which was the subject of my question above).

Thinking ‘aloud’, are symbols more like labels or more like pointers (in the programming sense)? Does it matter? Both ’empty labels’ and ‘null pointers’ would be eliminated along with their physical substrates. What about the opposite? What prevents a node from gaining too much centrality (which, according to my dilettante mind, represents an over-generalization)? Excitotoxicity? Nah, too radical. It’s more a symptom of pathology, and heralds cascading failures in the system. Then what else?

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